It is clear from the first knight move in game one, Kasparov wanted the match on his terms. In game two, he wants the match, but also on the machine's turf, now that the opportunity has knocked. He earned that breathing room. The computer rose to the challenge of forcing his breath.
Kasparov allows the Spanish Game (3. Bb5), as well as the Scotch (3. d4). Unlike the first game, in which Deeper Blue's opening book was soon exhausted by Kasparov's principled-yet-untread plan to start the game, Black allows the machine to draw moves from a database until 18.Qd2. Suprisingly, Kasparov achieves a closed position twenty-five moves into the game, the type that supposedly illuminates the strengths of the human savant as well the failings of mechanical pretenders. 23. Rec1!! put any illusions of positional ineptitude on Deeper Blue's part to rest; because of the opposition of the White rook to the Black queen, Black is forced to respond 23. .. c4, blocking the position in a way that allows only White to initiate action. After 25. Rca1, White stands better, but Black should have enough resources to draw.
Nonetheless, the machine expertly labored, containing Black's options through threats: first, on the queenside, and then on the kingside with 26.f4. The merits of 26. .. Nf6 vs. 26. .. f6 vs. 26. .. may be argued, but none could salvage the shuffling of pieces (31. .. Be7 and 32. .. Bf8) that followed. White invades the queenside and then firmly consolidates its positional advantage with 37. Be4.
45. Ra6 seals the win nicely. Efforts by Black to draw by perpetual check after 45. .. Qe3 are fruitless, as is the ending after 45. .. Qxc6 46. dxc6.
Overall, White's play was extremely solid, controlled, and most impressively denied its opponent counterplay with the touch of a grandmaster.